 Hi and welcome to the session. Let us discuss the following question. Question says, given that A vector dot B vector is equal to 0 and A vector cross B vector is equal to 0 vector. What can you conclude about the vectors A and B? Let us now start with the solution. Now we are given dot product of A vector and B vector is equal to 0. This implies A vector is perpendicular to B vector or A vector is equal to 0 vector or B vector is equal to 0 vector. We know if dot product of two vectors is equal to 0 then they are perpendicular to each other. If they are not perpendicular to each other then one of them is a 0 vector. So dot product of vector A and vector B is equal to 0 if they satisfy any one of these conditions. Now we are also given that cross product of A vector and B vector is equal to 0 vector. Now this implies A vector is parallel to B vector or A vector is equal to 0 vector or B vector is equal to 0 vector. We know if cross product of two vectors is equal to 0 vector then two vectors are parallel to each other. And if they are not parallel to each other then either of them is equal to 0 vector. So we can say cross product of these two vectors is equal to 0 vector if it satisfies any one of these three conditions. Now clearly we can see if vector A is not equal to 0 vector and vector B is also not equal to 0 vector then vector A cannot be perpendicular and parallel to the B vector. So we get dot product of vector A and vector B and cross product of vector A and vector B is equal to 0 if either vector A or vector B is equal to 0 vector. So we can write A vector dot B vector is equal to 0 and A vector cross B vector is equal to 0 vector if vector A is equal to 0 vector or vector B is equal to 0 vector. So we conclude that either magnitude of vector A is equal to 0 or magnitude of vector B is equal to 0. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.